Categorical Data Analysis

Abstract

The classical statistical tests are based on the initial formulation of two complementary hypotheses that are related to the parameters of the target population; these hypotheses are the null and the alternative hypotheses. The null hypothesis, denoted by H0, is the hypothesis that is to be tested. The alternative hypothesis, usually denoted by Ha, is the hypothesis that contradicts the null hypothesis (Rosner, 2010); usually, the alternative hypothesis will be related to a research hypothesis. To assess the null hypothesis, a sample of data is collected to compute a test statistic for supporting a decision in favor of or against the H0; there are four possible outcomes: 1. Evidence in favor of H0, with H0 in fact being true 2. Evidence against H0, though H0 is in fact true (Type I error) 3. Evidence in favor of H0, though H0 is in fact false (Type II error) 4. Evidence against H0, with H0 in fact being false In classical statistics, the probabilities of the occurrences of these outcomes are summarized in the following table: The general aim in hypothesis testing is to use statistical tests that make α and β as small as possible. Typically, the evidence against H0 is determined with a significance level less than or equal to 5%, while a statistical power of 80% or higher is considered adequate.